Self-synchronizing equalization techniques and systems

ABSTRACT

Methods and systems for processing received radio signals are described wherein the finite alphabet quality of digital transmissions is utilized to improve performance. Nonsynchronous sampling of received signals introduces intersymbol interference which is compensated for by these methods and systems. Different types of signal modulation, and their impact on this type of intersymbol interference are discussed. A robust diversity combining technique, usable in conjunction with antenna arrays is developed.

This application is a divisional of application Ser. No. 08/827,169,filed Mar. 27, 1997 now U.S. Pat. No. 5,937,014.

BACKGROUND

In recent years, wireless communication systems have been used to conveya variety of information between multiple locations. With digitalcommunications, information is translated into a digital or binary form,referred to as bits, for communications purposes. The transmitter mapsthis bit stream into a modulated symbol stream, which is detected at thedigital receiver and mapped back into bits and information.

In digital wireless communications, the radio environment presents manydifficulties that impede successful communications. One difficulty isthat the signal level can fade, because the signal may travel inmultiple paths. As a result, signal images arrive at the receiverantenna out of phase. This type of fading is commonly referred to asRayleigh fading or fast fading. When the signal fades, thesignal-to-noise ratio becomes lower, causing a degradation in thecommunication link quality.

A second problem occurs when the multiple signal paths are muchdifferent in length. In this case, time dispersion occurs in whichmultiple fading signal images arrive at the receiver antenna atdifferent times, giving rise to signal echoes. This causes intersymbolinterference (ISI), where the echoes of one symbol interfere withsubsequent symbols.

Raleigh fading can be mitigated by using diversity, such as antennadiversity, at the receiver. The signal is received on a plurality ofantennas. Because the antennas have slightly different locations and/orantenna patterns, the fading levels on the antennas are different. Inthe receiver, these multiple antenna signals are combined either beforeor after signal detection using such techniques asmaximal-ratio-combining, equal-gain-combining, and selective combining.These techniques are well known to those skilled in the art and can befound in standard textbooks, such as W. C. Y. Lee, Mobile CommunicationsEngineering, New York: McGraw-Hill, 1982.

The time dispersion can be mitigated by using an equalizer. Common formsof equalization are provided by linear equalizers, decision-feedbackequalizers, and maximum-likelihood sequence-estimation (MLSE)equalizers. A linear equalizer tries to undo the effects of the channelby filtering the received signal. A decision-feedback equalizer exploitsprevious symbol detections to cancel out the intersymbol interferencefrom echoes of these previous symbols. Finally, an MLSE equalizerhypothesizes various transmitted symbol sequences and, with a model ofthe dispersive channel, determines which hypothesis best fits thereceived data. These equalization techniques are well known to thoseskilled in the art, and can be found in standard textbooks such as J. G.Proakis, Digital Communications, 2nd ed. New York: McGraw-Hill, 1989.

Of the three common equalization techniques, MLSE equalization has beenconsidered preferable from a performance point of view. In the MLSEequalizer, all possible transmitted symbol sequences are considered. Foreach hypothetical sequence, the received signal samples are predictedusing a model of the multipath channel. The difference between thepredicted received signal samples and the actual received signalsamples, referred to as the prediction error, gives an indication of howgood a particular hypothesis is. The squared magnitude of the predictionerror is used as a metric to evaluate a particular hypothesis. Thismetric is accumulated for different hypotheses for use in determiningwhich hypotheses are better. This process is efficiently realized usingthe Viterbi algorithm, which is a form of dynamic programming.

Ideally, the diversity combining process and the equalization processshould be combined in some optimal way. Recent research has shown thatfor MLSE equalization, diversity combining should be done within theequalizer. This research can be found in W. H. Sheen and G. L. Stuber,"MLSE equalization and decoding for multipath-fading channels," IEEETrans. Commun., vol. 39, pp. 1455-1464, Oct. 1991; Q. Liu and Y. Wan "Anadaptive maximum-likelihood sequence estimation receiver with dualdiversity combining/selection," Ind. Symp. on Personal, Indoor andMobile Radio Commun., Boston, Mass., pp. 245-249, Oct. 19-21, 1992, andQ. Liu and Y. Wan, "A unified MLSE detection technique for TDMA digitalcellular radio," 43rd IEEE Vehicular Technology Conference, Seacaucus,N.J., pp. 265-268, May 18-20, 1993. In the above mentioned research,diversity combining is performed by adding together the magnitudesquared prediction errors from different diversity channels when formingmetrics.

The use of antenna arrays at base stations in a mobile communicationsystems has also been proposed as a technique for increasing capacityand performance. The most common approach for processing the informationgathered by each antenna associated with a particular signal is based ondirection of arrival (DOA) estimation followed by beamforming, i.e.combining the vector signal from the array to a scalar signal (spatialfiltering) before detection. However, this approach does not fullyexploit the spatial structure of the channel. A better way is to use analgorithm that is adaptive in the spatial domain and which also takesthe quality that the transmitted signal has a finite alphabet (e.g., 0'sand 1's) into account. Examples of such algorithms are the recentlyproposed iterative least squares with projections (ILSP) algorithm andthe decoupled weighted least squares with projections (DWILSP)algorithm. The decoupled algorithm is similar to ILSP in performance,but is computationally cheaper.

Both ILSP and DWILSP are, in their original formulation, limited to useon frequency-flat (i.e., non time-dispersive) channels. However, in manymobile communication systems, the channel cannot be modelled asfrequency-flat. To treat time-dispersive channels, extensions to theiterative least squares approaches have also been presented. Thesealgorithms are unfortunately quite complex, both regarding computationalaspects and detection procedures involved.

Another drawback associated with these conventional algorithms is theirrequirement of precise synchronization. Although the DWILSP algorithmcan be used to process signals received from unsynchronized cochannelusers, synchronization with the signal of interest is still assumed,i.e., the signal of interest is assumed to be sampled correctly inaccordance with the symbol timing. In practice, this assumption may nothold true, since perfect symbol timing is difficult to achieve. Forexample, in certain types of systems, e.g., time division multipleaccess (TDMA) systems which use short transmission bursts, proper sampletiming is extremely difficult to guarantee. Thus, as will be illustratedin the simulations performed by Applicants and described below, theconventional DWILSP algorithm suffers significant degradation (e.g.,increased bit error rate) when timing errors are introduced into thesampled signal.

Several techniques have been proposed which use oversampling, i.e.,taking more than one time discrete sample during each symbol interval,to handle the problems associated with unsynchronized signals. TheDWILSP algorithm, however, is designed to use only one sample per symbolinterval and, therefore, is not amenable to these types of solutions.

Accordingly, it would be desirable to provide a technique for estimatingsymbols using the DWILSP algorithm from unsynchronized signals sampledat the symbol rate. Moreover, it would also be desirable to use theDWILSP algorithm to obtain improved diversity combining.

SUMMARY

According to exemplary embodiments of the present invention, these andother drawbacks and problems associated with the conventional DWILSPalgorithm, and similar techniques for processing received radio signals,are overcome by providing self-synchronizing techniques which provideimproved performance for nonsynchronously sampled signals. For example,Applicants have recognized that nonsynchronously sampled signals createadditional intersymbol interference (ISI) which should be compensatedfor in order to improve detection performance. This additional ISI isdifferent than tat described above in that it is parameterizable (andtherefore readily determinable) based upon timing error and modulationtype.

Thus, exemplary embodiments of the present invention teach the provisionof compensation schemes which, for example, modify the conventionalDWILSP technique to compensate for the ISI introduced by nonsynchronoussampling. A specific example is given for MSK modulation, although thepresent invention can be applied to any type of modulation withadaptations which will be apparent to those skilled in the art.

In addition to providing self-synchronizing processing techniques,exemplary embodiments of the present invention also provide for robustdiversity combining which outperforms conventional techniques, e.g.,RAKE diversity combining. By using the DWILSP technique to providetemporal combining of spatio-temporal signal estimates created using anadapted version of the RAKE algorithm, exemplary embodiments of thepresent invention are able to significantly improve upon prior diversitycombining techniques.

BRIEF DESCRIPTION OF TEE DRAWINGS

The features and advantages of Applicants' invention will be understoodby reading this description in conjunction with the drawings, in which:

FIG. 1 is a block diagram of an exemplary cellular radio telephonesystem in which the present invention may be applied;

FIG. 2 illustrates an exemplary antenna array and processing structuresassociated therewith;

FIG. 3 is a flowchart depicting an exemplary self-synchronizingtechnique according to the present invention;

FIG. 4 is a graph illustrating simulation results in terms of bit errorrate for BPSK modulated signals processed according to both theconventional DWILSP technique and self-synchronizing techniquesaccording to the present invention;

FIG. 5 is a graph illustrating simulation results in terms of root meansquare delay for BPSK modulated signals processed according toself-synchronizing techniques according to the present invention;

FIG. 6 is a graph illustrating simulation results for MSK modulatedsignals processed according to both the conventional DWILSP techniqueand a self-synchronizing technique according to the present invention;

FIG. 7 is a graph illustrating simulation results for GMSK modulatedsignals processed according to both the conventional DWILSP techniqueand a self-synchronizing technique according to the present invention;

FIG. 8 is a block diagram of a conventional RAKE combiner;

FIG. 9 is a block diagram of another known RAKE combiner using theDWILSP technique to provide signal estimates;

FIG. 10 is a block diagram of a RAKE combiner according to an exemplaryembodiment of the present invention;

FIG. 11 is a block diagram of a RAKE combiner according to an anotherexemplary embodiment of the present invention;

FIG. 12 is a flowchart illustrating steps associated with an exemplarydiversity combining technique according to the present invention;

FIG. 13 is a graph illustrating the results of a first simulation usedto demonstrate the performance of an exemplar diversity combiningtechnique associated with the present invention; and

FIG. 14 is a graph illustrating the results of a second simulation usedto demonstrate the performance of an exemplary diversity combiningtechnique associated with the present invention.

DETAILED DESCRIPTION

The following description is scripted in terms of a cellularradiocommunication system, but it will be understood that Applicants'invention is not limited to that environment. To provide anunderstanding of various exemplary receivers and systems within whichstructures and techniques according to the present invention can beimplemented, the following summarizes an exemplary cellularradiocommunication system.

FIG. 1 is a block diagram of an exemplary cellular radiocommunicationsystem, including an exemplary base station 110 and mobile station 120.The base station includes a control and processing unit 130 which isconnected to the mobile switching center (MSC) 140 which in turn isconnected to the PSTN (not shown). General aspects of such cellularradiocommunication systems are known in the art, as described by theabove-cited U.S. patent applications and by U.S. Pat. No. 5,175,867 toWejke et al., entitled "Neighbor-Assisted Handoff in a CellularCommunication System," and U.S. patent application Ser. No. 07/967,027entitled "Multi-Mode Signal Processing," which was filed on Oct. 27,1992, both of which are incorporated in this application by reference.

The base station 110 handles a plurality of traffic channels through atraffic channel transceiver 150, which is controlled by the control andprocessing unit 130. Also, each base station includes a control channeltransceiver 160, which may be capable of handling more than one controlchannel. The control channel transceiver 160 is controlled by thecontrol and processing unit 130. The control channel transceiver 160broadcasts control information over the control channel of the basestation or cell to mobiles locked to that control channel. It will beunderstood that the transceivers 150 and 160 can be implemented as asingle device, like the traffic and control transceiver 170 in themobile station, for use with control channels and traffic channels thatshare the same radio carrier frequency. The traffic channels can be usedin a dedicated, connection-oriented manner to transmit information,e.g., for a voice connection, where each channel is used continuouslyfor a period of time to support transmission of a single stream ofinformation or in a packet-oriented manner where each channel can beused to send independent units of information associated with differentinformation streams.

Transceivers 150 and 160 may have dedicated antennas 170 and 180 which,using a duplex filter, transmit and receive signals for processingtherein. Alternatively, base station 110 may be provided with an antennaarray as depicted in FIG. 2. The antenna array will have some number mof antenna elements 200, where m>=2. Each signal creates a response oneach antenna element 200, which response is processed (e.g., filtered,downconverted, etc) in receive processing blocks 210. The processedsignal responses are used to generate a channel estimate h_(ik) and asignal estimate s_(k) (t) for each sampling time instance i as shown inblocks 220. The manner in which these estimates are created and combinedare described below with respect to exemplary embodiments of the presentinvention.

In order to have a complete understanding of the present invention, itis first beneficial to consider the origins thereof, in particular theDWILSP technique referred to above. A similar description of thisconventional technique can be found in the article entitled "DecoupledSeparation of Digitally Modulated Signals Arriving at an Antenna Array",authored by P. Pelin et al., published in Proc. of RVK 96, Lulea,Sweden, June 1996, the disclosure of which is expressly incorporatedhere by reference.

The Conventional DWILSP Technique

In an environment with multipath propagation, the output of an m-elementarray can be expressed as: ##EQU1## where d is the number of signalsimpinging on the array, s_(k) is the signal from the k:th user (withsymbols belonging to a finite alphabet) and γ_(kl) and τ_(kl) is theattenuation and time-delay for each of the q_(k) subpaths.

Herein, a narrow-band assumption is imposed (i.e., the propagationdelays associated with multipath are much smaller than the inversebandwidth of the signals), so that s_(k) (t-τ_(kl))≈exp(-jwτ_(kl))s_(k)(t). Equation (1) can thus be rewritten as: ##EQU2## where ##EQU3##called the spatial signature, is the sum of multipath array responsesdue to signal k. Assuming the d signals are symbol-synchronized, whichassumption (as mentioned above) increases the bit error rate associatedwith the received signal under many practical conditions, the antennaoutputs are passed through a filter matched to the transmit pulse, andsampled at the symbol rate R=1/T to yield the correspondingdiscrete-time model:

    x(n)=As(n)+v(n)                                            (3)

where A_(m)|d is the collection of total array response vectors, scaledby the signal amplitudes, i.e., A=[p₁ a₁ . . . p_(d) a_(d) ], s(n)=[b₁(n) . . . b_(d) (n)]^(T), b_(i) (n)=±1, and v(n) is spatially andtemporally white noise. A block formulation is obtained by taking Nsnapshots, yielding:

    X=AS(N)+V(N)                                               (4)

where X_(m)|N (N)=[x(1) . . . x(N)], S_(d)|N (N)=[s(1) . . . s(N)], andV_(m)|N)=[v(1) . . . v(N)]. The spatial structure of the data isrepresented by A, while the matrix S represents the temporal structure.The above formulation is valid for BPSK (binary phase shift keying)signals, but extension to arbitrary linear modulation schemes isstraightforward.

By defining one signal (at a time) to be signal of interest (SOI),equation (4) can be rewritten in the following way: ##EQU4## where thefirst signal is taken to be the SOI, without loss of generality. Theterm J(N) thus corresponds to interfering signals plus noise. Since itis desired to estimate the signals with little or no spatial knowledge,a and s can be iteratively estimated, based on the formulation inequation (5).

Given an initial estimate of a spatial signature a, the followingweighted least-squares criterion function is iteratively minimized:##EQU5## Here, W should ideally be chosen as, ##EQU6## which can beinterpreted as a prewhitening of the data vector x(n). However, it canbe shown using the matrix inversion lemma, that using the inverse of thesample estimate of the covariance of the array output producesasymptotically equivalent signal estimates. Equation (6) can thus bereformulated as follows: ##EQU7## with ##EQU8## and ##EQU9## For fixedb, the solution to equation (7) with respect to s is ##EQU10##Exploiting the finite-alphabet property, this solution is projected ontoits closest discrete values in the signal space. In the case of BPSKsignals, this projection is equivalent to taking the sign of eachcomponent in s. The (modified) spatial signature b is then updated byminimizing equation (7) with respect to b. The solution is: ##EQU11##

Note that equation (9) is a temporally matched filter to the currentsignal estimate, whereas (8) represents a spatially matched filter. Theprocess is repeated until s converges, after which the algorithmcontinues with the next signal.

As mentioned above, the conventional DWILSP algorithm does not take intoconsideration that the symbol sampling is imperfect. Accordingly, thepresent invention modifies the aforedescribed technique to handleintersymbol interference caused either by non bit-synchronized samplingor by the modulation technique used to process the original signal fortransmission over the air interface. These modified techniques accordingto the present invention are referred to herein as "self-synchronized"techniques.

Self-Synchronized Techniques

Sampling a signal in an unsynchronized manner means, for most modulationformats, that intersymbol interference (ISI) is introduced. This form ofISI is quite different from the ISI caused by a time dispersivepropagation channel. The reason for this is that ISI caused byunsynchronized sampling has an underlying structure, i.e., the ISI canbe parameterized by the timing error.

The parameterization of this structured kind of ISI differs betweenmodulation formats. Therefore, the modifications made to the DWI=SPtechnique according to exemplary embodiments of the present inventionwill also depend on the modulation format.

The effects of ISI due to nonsynchronous sampling are reflected in thedata model by a modification of the source signal description as:##EQU12## Here, the ISI is parameterized in the scalar signal s_(ISI),i(n), and the characterization of this ISI depends on the modulationformat. In some cases, there is no ISI at all, for example MPSKmodulation with a rectangular pulse shape, sampled directly at thesymbol rate without a preceding matched filter. Nevertheless, in mostcases, sampling nonsynchronously leads to ISI, as for example when asignal modulated by minimum shift keying (MSK) is nonsynchronouslysampled.

An MSK signal is most often received by direct sampling at the symbolrate, without any matched filter, as in the European GSM system andsystems operating in accordance with the GSM standard. Generally, thereceived signal, nonsynchronously sampled, can be expressed as:##EQU13## where T_(s) is the sampling interval and τε[0,1] is the timingerror in the sampling (relative to T_(s)). From this equation it can beseen that for an MSK-signal, the signal s_(ISI) (t) is characterized by:

a constant envelope, that is, it has the same power independent of thevalue for τ;

the ISI-components are separated in quadrature, where: ##EQU14## is thein-phase component, and ##EQU15## is the quadrature component. Thesequalities make it possible to write the output, x(t), from the m-elementarray antenna for a flat fading channel or a spatio-temporal diversitypath as: ##EQU16## where, ##EQU17## x(t)εC^(mx1), and hεC^(mx1)describes the propagation channel for a flat fading channel (i.e.,without time dispersion) or a spatio-temporal diversity path. Finally, Jdenotes any modeling error. To provide even better performance, apre-whitening process can be applied. Pre-whitening is achieved bycomputing the following new quantities. First, the estimated arraycovariance matrix is defined by (with "H" denoting the Hermiteantranspose operator): ##EQU18## and then the pre-whitened array outputdata and channel response vector as, resp., ##EQU19## and, ##EQU20## Theself-synchronizing technique according to the present invention fordetecting/estimating ISI in a single diversity path can now be outlinedas follows. The flowchart of FIG. 3 provides a visual guide to the belowdescribed steps according to the present invention.

Assume, at block 300, an initial timing error, e.g., τ=0.5, and create acorresponding signal r_(ISI) (t), using a known training/referencesequence r(t) (which is contained as a part of the original finitealphabet signal, s(t), transmitted from a mobile station). Those skilledin the art will appreciate that different systems provide differentknown reference sequences in their transmission bursts. For example, theGSM system provides a training sequence having 26 bits.

To continue for the general case, generate, for t=t₁ up to t=t₂, theconstruction denoted r_(ISI) (t):

    r.sub.ISI (t)=r(t)-j·r(t-1)                       (18)

the length of this construction will depend on the actual length of theparticular training sequence considered. Use this construction, togetherwith the well-known Least-Squares (LS) method for parameter estimation,to find an initial estimate, g, of the channel response vector at block310 using the below data model (with t=t₁ . . . t₂):

    z(t)=g·r.sub.ISI (t)                              (19)

Having found an initial estimate, the process continues iterativelybeginning with an estimation of the sampled ISI signal, s_(ISI) (t),employing the LS-method using the received pre-whitened data, z(t), andthe estimated channel response vector, g, as indicated at block 320.Next, the model for the estimated received data can be rewritten as:##EQU21## where s(t) is the originally transmitted finite alphabetsignal by a mobile station. In equation (20), the variables α₁, α₂ ands(t) can then be solved for using the conventional DWILSP technique. Therelative sampling instance, τ, can be estimated from α₁ and α₂.

The next step is to compute an updated estimate of the sampled ISIsignal according to:

    s.sub.ISI =α.sub.1 ·s(t)-j·α.sub.2 ·s(t-1)

Then an updated channel response vector, g, can be computed, block 330,using the LS-method on the data model:

    z(t)=g·s.sub.ISI (t)                              (21)

If s(t) has converged as determined at block 340, then the process canbe terminated, otherwise another iteration begins at step 320.

Other linear modulation formats, e.g., BPSK, lead to models similar tothe one presented above for MSK. Note, however, that the ISI parametervector may or may not be a linear function of timing error τ_(i) forthese other models.

To test the performance of processing techniques according to thepresent invention, a simulation was conducted that compares the presentinvention with the conventional DWILSP algorithm for signals using BPSKor Gaussian MSK modulation. The test simulated a 5-element antenna arraythat receives two signals from nominal DOA:s of [-15°,20°]. The signalsare transmitted in bursts corresponding to the normal GSM burst, i.e.,148 bits, including a 26 bit training sequence in the central part, andthree known tail bits at each end. The channel was modelled asflat-fading and the scattering cluster width σ was 3° To simulateRayleigh fading, independent channel vectors were used for eachtransmitted burst. The average E_(b) /N_(o) at each antenna-element wasset to 5 dB.

In the BPSK case, the performance of the original DWILSP algorithm wascompared to the self synchronizing technique according to the presentinvention. In the simulation, the self-synchronizing technique wastested twice, once using the LS-approach, and a second time usingViterbi equalization to facilitate a performance comparison. The timingerror introduced by nonsynchronous sampling was varied, giving theresults shown in FIG. 4. In this figure, bit error rate is plottedagainst tiring error. Throughout these simulations the followingconventions are used. The dashed line represents the results for theconventional DWILSP technique, the results for the self-synchronizingtechnique (LS-approach) is shown as a dotted line and the results forthe self-synchronizing technique (Viterbi approach) is shown using asolid line.

In FIG. 4, it can be seen that either implementation of the presentinvention provides improved performance as compared with theconventional DWILSP technique due to its assumption of synchronized bitsampling. The numerical problems involved in the LS implementation fortiming errors in the vicinity of τ=0.5 can be seen by the spike in theBER. Using the Viterbi algorithm also leads to a performance degradationfor τ≠0 and τ≠1, but this is a consequence of the signal power lossinvolved, and not the Viterbi algorithm itself. In some signalprocessing applications, for example radar and positioning, the timingerror τ is of more importance than the BER. FIG. 5 shows the root meansquare (RMS) error of the delay estimate for the LS and Viterbiimplementations of the present invention.

Repeating the simulation described above but with MSK and GMSKmodulation for the transmitted signals provides the results shown inFIGS. 6 and 7, respectively. For both types of modulation, the presentinvention again outperforms the DWILSP technique. For the GMSK case, itcan be seen that the performance of the self-synchronizing techniqueaccording to the present invention is only slightly dependent on thetiming. The best performance is obtained by sampling the received signalbetween symbol transitions, i.e. τ=0.5, since the GMSK waveform is muchcloser to MSK at these instants.

As can be seen from the foregoing, the conventional DWILSP algorithmrequired the signal of interest to be sampled correctly or the BERperformance will be degraded. By way of contrast, exemplary techniquesaccording to the present invention provides improved performance acrossthe spectrum of timing errors and, accordingly, permit the signal ofinterest to be sampled nonsynchronously. For some modulation formats,some performance degradation is introduced, whereas for others, there isno performance degradation involved.

The self-synchronizing techniques according to the present inventionalso provide an estimate of the timing error, either explicitly, or as afunction value thereof. For example, Equation (13) can be rewritten toprovide an estimate of the timing error τ as the following functionvalue: ##EQU22## where T_(s) is here a known quantity, and α₁ has beenestimated by the conventional DWILSP algorithm. As a consequence, theself-synchronizing version of the DWILSP algorithm can be used for otherapplications than communications, for example radar and positioning.

Diversity Combining

The foregoing exemplary embodiments dealt with ISI caused by modulationand/or unsynchronized sampling. This type of ISI is deterministic sincethere is a strict underlying parameterization. The following exemplaryembodiments relate to ISI caused by the propagation channel which, asdescribed above, is quite different in nature. In the same way that themobile radio channel spreads the transmitted energy in the spatialdomain, i.e., in a stochastic manner, the time-dispersion of the channelalso causes a spreading of energy in the temporal domain.

Cancelling the effect of the channel dispersion is, as described above,a classical problem known as equalization. Conventional techniquesinclude different filtering approaches, such as the linear equalizer (afilter approximating the inverse of the channel) and the decisionfeedback equalizer (DFE). These can be extended to the array signalcase. Another often employed algorithm is the maximum likelihoodsequence estimator (MLSE). The latter is often regarded as beingoptimal, as it is derived from the maximum likelihood principle.

As described above, the conventional DWILSP algorithm acts as a spatialdiversity combiner, collecting the spatially spread energy in anefficient way. S Thus, it would be desirable in the case of a channelspreading the transmitted energy both in space and time, to design analgorithm that performs diversity combining jointly over space and time.Such algorithms have been proposed but are unfortunately quite complex,both with regard to computational aspects and detection proceduresinvolved. Also, these conventional approaches require an oversampling ofthe received signal. However, based on the well-known RAKE-approach, aspace-time algorithm according to the present invention can be derivedwith the DWILSP algorithm as its elementary building block.

Regarding the source signals as temporally white, the time dispersivecase can be reformulated according to the frequency flat data model. TheDWILSP algorithm can then be adopted to estimate different time-arrivalsseparately. This step thus performs spatial combing. Then, the differenttime-arrival estimates are combined temporally. This technique accordingto the present invention thus constitutes a RAKE-combiner, exploitingboth the spatial and temporal structure of the measured array signal, aswell as the finite alphabet property of the modulated source signal.Moreover, this novel technique provides high performance at a lowcomputational complexity, while at the same time lending itself to asimple and straightforward implementation.

The approach taken here is based on estimation of different timearrivals of the desired user signal separately, instead of trying toinvert or equalize the filter representing the channel. A final estimateis achieved by a combination of the estimates of the different timearrivals.

To provide a foundation for understanding diversity combining accordingto the present invention, traditional RAKE techniques are firstdescribed. The RAKE combiner was originally proposed for direct sequencespread spectrum (DSSS) systems operating on time-dispersive channels.Consider the data model for a frequency selective channel: ##EQU23##where s is a DSSS signal. A significant property of DSSS signals is thatthey are wideband signals. The wideband property is achieved byspreading the original data sequence with a high rate spreading code,whose elements are called chips, each with a duration of T_(c) seconds.Each original data symbol thus contains several chips, and the spreadingcode is designed to have an autocorrelation function resembling whitenoise, such that symbols shifted more than one chip length apart areapproximately uncorrelated. This type of signal is commonly used, forexample, in radiocommunication systems that operate in accordance withcode division multiple access (CDMA) techniques.

The DSSS RAKE combiner estimates each time-arrival s(n-kT_(c)) byexploiting the autocorrelation property of the spreading sequence. TheL+1 signal estimates are then temporally combined to yield a finitesignal estimate. The total scheme is thus equivalent to an L+1 orderdiversity combiner (if the channel taps h_(k) are uncorrelated). Theconventional RAKE combiner can be illustrated as in FIG. 8, where eachblock 800 provides a time delay T_(c) and the multiplication by c(n) ateach multiplier 810 represents the despreading operation. The temporalbranches seen in FIG. 8 are often referred to as "RAKE fingers" but arereferred to herein as "spatio-temporal signal estimates" when used torefer to branches of a modified RAKE combiner wherein the DWILSPalgorithm is used to provide for spatial combination. The outputs ofeach RAKE finger are then temporally combined at block 820 by adiversity combining technique as will be described below.

Now consider the array signal model for the single user, frequencyselective case: ##EQU24##

The RAKE approach can also be applied to the array (unspread) signalcase. Instead of spread symbols, as in the DSSS data model of equation(22), consider blocks of symbols. If the user signal is sufficientlytemporally white, shifted versions, by an amount of T_(s) seconds ormore, become approximately uncorrelated. A block of symbols thus acts asthe spreading sequence in the DSSS case, and different time-arrivals canbe viewed as different user signals in the frequency flat case. Then theDWILSP type algorithm can be used to estimate the different timearrivals separately.

The RAKE approach can be generalized to the multi-user case. Consideringthe different time arrivals as different signals, the double sum in themulti-user model can be rewritten according to equation (22),corresponding to the frequency flat case with d(L+1) users: ##EQU25##Thus, the RAKE combiner for the array signal case is shown in FIG. 9,where delayed versions of the received symbols are provided by blocks900. The despreading operation in FIG. 8 is replaced by the conventionalDWILSP algorithm in blocks 910 which provide spatio-temporal signalestimates to the temporal combining block 920.

Applying the conventional DWILSP algorithm to estimate time arrival k inthe model of equation (23), it is seen that with a known temporallywhite user signal, the estimate of h_(k) is still consistent. However,the filter tap correlations introduce an ISI term into the signalestimate in a manner similar to that described above.

To overcome this problem associated with prior RAKE combiner efforts,i.e., to mitigate the effect of filter tap correlation, theself-synchronizing techniques described in the above exemplaryembodiments can be applied to provide the spatio-temporal signalestimates as shown in FIG. 10. Therein, the delay blocks 1000,spatio-temporal signal estimators 1010 and temporal combining logic 1020operate as described above.

In the case of DSSS, maximum ratio combining (MRC) is often employed asthe temporal combining technique employed in block 820 of FIG. 10. MRCmaximizes the output signal-to-noise ratio (SNR), given independentnoise in each finger and uncorrelated filter taps. The combined signalestimate is given as: ##EQU26## where s_(k) (n) is the output of thek:th finger, h_(k) ^(*) the conjugate of the corresponding filter tap,and σ_(k) ² is the finger noise variance.

Modified Maximum Ratio Combining

As described in the above incorporated by reference article entitled"Decoupled Separation of Digitally Modulated Signals Arriving at anAntenna Array", the conventional MRC approach can be modified with theconventional DWILSP algorithm. For example, before projection onto thefinite symbol alphabet, the k:th estimate of the i:th user signal afterthe final iteration can be expressed as:

    s.sub.ik (n)=α.sub.ik s.sub.ik (n)+β.sub.ik (n) (26)

where α_(ik) represents a small bias (usually negligible), and β_(ik)(n) is a noise term due to scaled thermal noise v(n) plus cochannel andself interferences s_(jl) (n), (j≠i) OR (l≠k). This noise term can, withgood accuracy, be considered as temporally white Gaussian and the noisein different signal estimates are approximately uncorrelated, i.e.E[β_(jl) β_(ik) ]=0, for (j≠i) OR (l≠k).

Ignoring the bias a, each signal estimate of s_(i) (n) is automaticallynormalized in amplitude (PSK: |s(n)|=1) by DWILSP. Furthermore, as thenoise terms β(n) are uncorrelated between branches, one way of combiningthe estimates would be to use MRC at equation (25) as shown below:##EQU27## In equation (27), the operator (Proj) means projection ontothe finite alphabet and σ² _(ik) is the variance of β_(ik) (n), whichcan be estimated as Var(Proj(s_(ik))-s_(ik)). For BPSK modulation,DWILSP projects symbols onto the alphabet of +/-1 and only the varianceof the real part of the noise should be considered.

However, when DWILSP falls completely at estimating a time-arrival of asignal, for example when a tap h_(k) in equation is weak or doesn'texist, the false signal estimate is still normalized in amplitude,resulting in noise saturation effects, i.e. the variance σ² of β(n)reaches a limit. To suppress bad estimates/fingers, simulations haveindicated that a better weighting tan ordinary MRC is: ##EQU28##

Note that the value of the exponent (i.e., 4) in equation (28) is notcritical. Any value in the range 3-6 results in approximately the samebit error rate (BER).

Temporal Combining Using DWILSP

Although the DWILSP algorithm was originally intended for applicationswith antenna arrays, Applicants have recognized that this technique isalso a general diversity combiner. Consequently, the conventional DWILSPtechnique can also be used for the temporal combining function depictedin blocks 820, 920 and 1020 of FIGS. 8-10, respectively. These exemplaryembodiments of the present invention are illustrated in FIG. 11, whereinblocks 1100 provide delayed samples, blocks 1110, which are labelledsimply as estimators to reflect a generic inclusion of traditional RAKEfingers, conventional DWILSP spatio-temporal estimators or usage of theself-synchronizing techniques according to the present invention,provide signal estimates and block 1120 shows the DWILSP techniquefunctioning as the temporal combiner. Used in this way, stacking the L+1(soft) estimates s_(ki) of user signal i, a matrix equation is obtainedas: ##EQU29## where the left hand side of the matrix corresponds to themeasured array signal X, s is the true signal and Q is a noise term. Thecolumn vector w can be interpreted as a temporal channel vector,representing the delay profile of the channel. The column vector w alsohas a direct correspondence to the combining weights h_(k) ^(*) /σ_(k) ²in MRC, or 1/σ_(k) ⁴ in the modified scheme, as solving equation (29)using DWILSP is essentially a search for the best diversity combiningweights. Note that with the DWILSP algorithm employed for temporalcombining, as well as to provide the spatio-temporal signal estimates,the finite alphabet property is used twice.

There are several benefits associated with using the DWILSP techniquefor temporal combining in a RAKE receiver. For example, DWILSP is veryrobust in cases where not all diversity channels contain the signal ofinterest. Also, there is no specific assumption made regarding noisecolor, and the amount of fading correlation. Regardless of the temporalcombining scheme applied, however, tracking of the combining weights forblocks/bursts of data, is desirable as it provides valuable informationabout time variations of the effective channel length. Also, thisinformation is useful for frame synchronization in TDMA systems.

To summarize the novel diversity combining techniques according to thepresent invention, an exemplary series of steps is illustrated by way ofthe flowchart of FIG. 12. First, at block 1200, the known trainingsequence (e.g., the CDVCC in D-AMPS) is used to obtain synchronization,and estimate the filter length L. Then, initialized with the trainingsequence, the self-synchronizing technique described above can be usedto obtain a signal estimate s_(ik) of time path k at block 1210. Next,the signal estimates can be temporally combined at block 1220, by either(1) estimating the variance of β_(ik) (t) and using modified MRCaccording to equation (28) or using the conventional DWILSP to performtemporal combining.

The performance of RAKE receivers according to the present invention wasevaluated numerically at two different settings of a 5-tap FIR channel.The local scatter model was used to model each filter tap. The filtertaps were modelled as statistically independent, therefore and thestandard version of the DWILSP algorithm was used to provide thespatio-temporal signal estimates.

In the simulations, the receiving antenna was chosen to be a 10-elementuniform linear array (ULA). Three equally powered cochannel users wereplaced at nominal DOA:s [30°, 0°, 45°], relative to the array broadside.BPSK data was transmitted in bursts of 150 bits. Each burst included a15-bit m-sequence, periodically extended to 19 bits, which was used as atraining sequence for initialization of the receiver algorithm.

As a comparison, the performance of the conventional MLSE technique wasalso evaluated. The MLSE was run twice: once with the exact channel andinterference covariance matrix as a benchmark, and also using maximumlikelihood estimates of these parameters obtained from the trainingsequence to provide a more realistic evaluation of MLSE performance. TheMLSE was implemented with the Viterbi algorithm.

In the first simulation, the relative average power in each tap was thesame. Assuming a larger angular spread for the late arrivals (but thesame nominal DOA), the cluster width standard deviations for thedifferent taps were [2°, 3°, 4°, 5°, 6°]. The total signal power is heredefined as the sum of the powers in each filter tap. The resulting BERfor the user at 0=0° as a function of the element E_(b) /N_(o) is shownin FIG. 13.

Therein, starting from top right, the first curve shows the performanceof the MLSE run with estimated channel parameters and interferencecovariance, and it is seen that this method has a performance that islimited by the cochannel interference. This characteristic is not seenin the other curves. The second curve shows the performance of theRAKE-combiner using standard MRC temporal combining. Moving to the thirdcurve from the top right, it is seen that performance has been improvedby about 2 dB using modified MRC. Another 2 dB is gained by employingDWILSP combining. The last curve shows the performance of the MLSE runwith the exact parameters. Considering the fact that the MLSE is runwith estimated parameters in a practical application, e.g. the firstcurve, the RAKE-combiner using DWILSP as the temporal combining yieldsvery good performance.

In the second simulation, FIG. 14, the channel setting was adjusted tosimulate a hilly terrain environment. The mean filter tap powers wereset as [0, 0, -20, -20, -6] dB and the cluster width standard deviationswere [2°, 3°, 6°, 2°]. Each tap corresponded to a direction of [0°, 1°,0°, 0°, 10°] relative to the nominal DOA's, i.e., the late arrivalimpinging from a somewhat different direction compared to the earlyones. The relative performance of the different algorithms resemble theresults from FIG. 13. But this time, with an easier channel setting, thedifference in performance between the DWILSP-RAKE and MLSE usingestimated parameters is larger. In fact, the DWILSP-RAKE comes close tothe MLSE run with the exact parameters at high signal-to-noise ratios.

It is, of course, possible to embody the invention in specific formsother than those described above without departing from the spirit ofthe invention. The embodiments described above are merely illustrativeand should not be considered restrictive in any way. The scope of theinvention is determined by the following claims, rather than thepreceding description, and all variations and equivalents which fallwithin the scope of the claims are intended to be embraced therein.

What is claimed is:
 1. A RAKE receiver comprising:an input node forreceiving signal samples; a plurality of delay devices for generatingdelayed versions of said signal samples; a plurality of estimationbranches, each receiving one of said delayed versions of said signalsamples, and each for estimating a sample value therefrom; and atemporal combining unit for receiving said estimated sample values fromsaid plurality of estimation branches, wherein said temporal combiningunit uses a decoupled weighted iterative least squares with projections(DWILSP) algorithm to combine said estimated sample values.
 2. The RAKEreceiver of claim 1, wherein at least one of said plurality ofestimation branches uses said DWILSP algorithm to estimate itsrespective sample value.
 3. The RAKE receiver of claim 1, wherein atleast one of said plurality of estimation branches uses a modifiedversion of said DWILSP algorithm which mitigates intersymbolinterference introduced by filter taps to estimate its respective samplevalue.
 4. A RAKE receiver comprising:an input node for receiving signalsamples; a plurality of delay devices for generating delayed versions ofsaid signal samples; a plurality of estimation branches, each receivingone of said delayed versions of said signal samples, and each forestimating a sample value therefrom, at least one of said estimationbranches using a modified version of a decoupled weighted iterativeleast squares with projections (DWILSP) algorithm to estimate itsrespective sample value, wherein said modified version operates tomitigate intersymbol interference introduced by filter taps; and atemporal combining unit for receiving and combining said estimatedsample values from said plurality of estimation branches.
 5. The RAKEreceiver of claim 4, wherein said temporal combining unit uses saidDWILSP algorithm to combine said estimated sample values.
 6. The RAKEreceiver of claim 4, wherein said temporal combining unit uses a maximalratio combining technique to combine said estimated sample values.